One way of internalizing the externalities that each individual bank imposes on the rest of the financial system is to impose capital surcharges on them in line with their systemic importance. Given the complexity of the financial system and the resulting difficulties in measuring systemic importance, it is sometimes argued that higher capital surcharges should be applied to larger banks, abstracting from other factors like interconnectedness. In this paper, the authors consider different network structures of the banking system that are characterized by two different centrality measures. Their main finding is that size alone is not always a good proxy for systemic importance: it must be supplemented with detailed information on interbank exposures. A relatively small bank playing an outsized role in the interbank market might be more systemic, and thus garner a higher capital surcharge, than a less-connected bank of somewhat larger size. Alternatively, if the centrality of banks in an interbank network is positively correlated with their size, then proxies of a bank's systemic importance largely based on size are sufficient indicators.